不等式

Viability Theory is applied to the optimal control problem for switching time varying systems in this dissertation for the first time. The statement about a characterization of the extended value functions as the unique lower semicontinuous solution to a Bensoussan-Lions type QVI is proved.

本文首次将生存理论这一数学工具应用到有限时间切换时变系统的最优控制问题中，得到了最优控制问题的值函数是一类拟变分不等式唯一的下半连续解的重要结论。

The key of our method is to reduce the exact controllability of a semilinear system to the observability estimate for the dual system of its linearized system.

另一方面，我们注意到，上述的两种方法无法给出任何能观性不等式中出现的常数的显式估计，因为它们采用的是反证法来吸收低阶项的。

In Chapter 3 Firstly, the exponential stability in mean square and almost sure exponential stability for neutral stochstic neural networks with time-varying delay can be discussed by using the linear matrix inequality and the semimartingale convergence theorem; And our sufficient conditions are less conserative; Secondly, by utilizing the fixed point theorem, some sufficient and necessary conditions ensuring the asymp- totic stability in mean square for neutral stochastic neural networks with time-varying delays can be given.

第三章首先，利用线性矩阵不等式方法和半鞅收敛定理，考虑了一类具变时滞中立型随机神经网络的二阶矩指数稳定性和几乎必然指数稳定性，所得到的条件保守性要好；其次，采用不动点方法，给出了具变时滞中立型随机神经网络的二阶矩渐近稳定性的充要条件。

In Chapter Ⅱ,Heisenberg's inequality under the frame-work of separable Hilbertspace(essentially 〓space)is under consideration.

第一章考虑在可分的Hilbert框架下的Heisenberg不等式。

It was proved that the design of the observer and the state feedback controller of the augmented system satisfied separation principle.

证明了观测器与增广系统状态反馈的设计满足分离原理，利用线性矩阵不等式给出了相应的控制器的设计。

The existence theorem of generalized weak efficient solutions with respect to variable, cone for a linear G〓teaux differentiable mapping is proved with set valued mapping fixed-point theorem and the relation between a vector optimization and a variational inequality problem. The existence of weak efficient solutions for multi-objective convex vector optimization is characterized.

建立映射在线性G〓teaux可微条件下关于可变锥的广义弱有效解的存在性及多目标凸向量优化问题在G〓teaux可微条件下弱有效解的特征，利用集值映射不动点定理及向量优化与变分不等式的关系证明线性G〓teaux可微锥凸映射关于可变锥的广义弱有效解的存在性定理。

Most geometric inequalities concerning convex bodies have the property that the occurence of the equality sign characterizes geometrically significant objects, like balls , ellipsoids .

中文摘要：在几何中，大多几何不等式都有这样一个性质：当取一些特殊的凸体时，比如球，圆，椭球等，等号成立。

The results show that the effective methods to deal with the LMIs are the matrix transformation, similarity transformation and Schur's Complement Lemma.

线性矩阵不等式可以有效地用内点法进行数值求解，目前已成为研究控制问题的一种重要工具。

By using the exist- ence result of VF- ICP and VF - IVIP with single - valued mappings and the continuous selection theorem due to Ding,Kim and Tan, solution existence for GVF- ICP and GVF- IVIP is derived under suitable assumptions.

通过具单值映象的向量F-隐补问题和向量F-隐变分不等式问题解的存在性的研究和使用Ding，Kim和Tan的连续选择定理，在适当假设下证明了CVF-ICP和GVF-IVIP解的存在性，推广了其他人的结果。

Secondly, we conside some kinds of projection iterative schemes for variational inequality problem ≥0, which divide to two aspects, one is S is the single-valued operator, the other is S is the multi-valued.

其次，讨论了变分不等式≥0中S为单值算子和多值算子情况下的几种投影迭代算法。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。